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An isotropic radiator of power \( P \) produces at distance \( r \) a power density of

  • A.\( P/(4\pi r^2) \)
  • B.\( P/(2\pi r^2) \)
  • C.\( P/(4\pi r) \)
  • D.\( P r^2/(4\pi) \)

Answer: A

The power spreads uniformly over the whole sphere of area \( 4\pi r^2 \), which is the definition of an isotropic radiator. Real antennas concentrate power in some directions, and the ratio to the isotropic density is the gain.

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